CS201 Data Structures Lecture 11
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Questions and Answers

What are the three cases for deleting a node in a Binary Search Tree (BST)?

  • Node with zero children, Node with two children, Node with three children
  • Node with one child, Node with two children, Node with three children
  • Node with one child, Node with three children, Node with four children
  • Node with zero children, Node with one child, Node with two children (correct)

    • How is the deletion of a node with zero children handled in a BST?

    Simply delete the node.

    What is the process of deleting a node with one child in a BST?

    Connect the child node with the parent node of the deleted value.

    When deleting a node with two children in a BST, what are the two key rules used?

    <p>InOrder Predecessor and InOrder Successor.</p> Signup and view all the answers

    The InOrder Predecessor rule requires you to delete the node with two children and replace it with the largest value on the right subtree of the deleted node.

    <p>False</p> Signup and view all the answers

    The InOrder Successor rule requires you to delete the node with two children and replace it with the lowest value on the right subtree of the deleted node.

    <p>True</p> Signup and view all the answers

    What is the default parameter value for 'val' in the parameterized constructor of a Binary Search Tree (BST) class?

    <p>None</p> Signup and view all the answers

    What is the primary purpose of traversing a Binary Search Tree?

    <p>To visit all the nodes in the tree in a specific order</p> Signup and view all the answers

    Which of these statements accurately describes the process of searching in a BST?

    <p>It is based on the value of nodes, navigating left or right depending on the comparison with the root</p> Signup and view all the answers

    What is the core concept behind the efficiency of searching in a BST?

    <p>The BST property allows for efficient searching by systematically eliminating half of the search space at each comparison.</p> Signup and view all the answers

    What is the approach for finding the minimum value in a BST?

    <p>Traverse from root to left recursively until a node with no left child is encountered</p> Signup and view all the answers

    In a BST, the height is entirely controlled and never depends on the order of element insertions.

    <p>False</p> Signup and view all the answers

    Unbalanced BSTs are not a concern as they maintain optimal search performance regardless of their structure.

    <p>False</p> Signup and view all the answers

    Why are balanced BSTs preferred over unbalanced BSTs?

    <p>Balanced BSTs maintain a height that is logarithmic to the number of nodes, ensuring efficient search, insertion, and deletion operations.</p> Signup and view all the answers

    What is the primary issue addressed by AVL trees and other self-balancing BST implementations?

    <p>Preventing the creation of unbalanced trees</p> Signup and view all the answers

    What is the key characteristic of an AVL tree that distinguishes it from other BSTs?

    <p>An AVL tree is a self-balancing binary search tree where the height difference between the left and right subtrees of any node is limited to -1, 0, or +1.</p> Signup and view all the answers

    Explain what the balance factor of a node in an AVL tree represents.

    <p>The balance factor of a node is the difference in height between its left subtree and right subtree, giving an indication of the node's balance.</p> Signup and view all the answers

    What is the primary purpose of using balance factors in AVL trees?

    <p>To maintain a balanced tree structure and prevent unbalance</p> Signup and view all the answers

    An AVL tree with a balance factor of 1 is considered balanced.

    <p>True</p> Signup and view all the answers

    Which of these statements is TRUE about the efficiency of AVL trees compared to unbalanced BSTs?

    <p>AVL trees maintain consistent log(n) time complexity for operations</p> Signup and view all the answers

    AVL trees are named after Adelson Velskii and Eugene Landis, who introduced the concept in 1960.

    <p>False</p> Signup and view all the answers

    AVL tree is a self-balancing binary search tree exclusively designed for efficient memory management.

    <p>False</p> Signup and view all the answers

    What is the primary difference between AVL trees and other self-balancing BST implementations such as red-black trees and splay trees?

    <p>While all these implementations are self-balancing, they employ different algorithms and heuristics for achieving and maintaining balance.</p> Signup and view all the answers

    AVL trees are always guaranteed to be perfectly balanced at any given time.

    <p>False</p> Signup and view all the answers

    Explain the role of rotations in AVL trees.

    <p>Rotations are the core mechanism used in AVL trees to maintain balance. They involve rearranging nodes to adjust the height difference between subtrees and ensure that the balance factor remains valid.</p> Signup and view all the answers

    The term ‘avl’ in AVL tree refers to the discoverers’ surnames, George M. Adelson and Eugene M. Landis

    <p>False</p> Signup and view all the answers

    The height difference between the left and right subtrees of any node in an AVL tree is always either 0 or +1 or -1.

    <p>True</p> Signup and view all the answers

    Which of these statements about AVL tree operations is TRUE?

    <p>AVL trees maintain consistently efficient search, insertion, and deletion operations.</p> Signup and view all the answers

    AVL trees are used to implement a variety of data structures, including associative arrays, maps, sets, and similar interfaces.

    <p>True</p> Signup and view all the answers

    What is the significance of ensuring a balanced AVL tree in practice?

    <p>A balanced AVL tree guarantees efficient search, insertion, and deletion operations, maintaining a logarithmic time complexity and ensuring consistent performance, even with a large number of elements.</p> Signup and view all the answers

    Which of the following statements is TRUE about AVL trees?

    <p>AVL trees offer a trade-off between efficiency and complexity, offering a balance between the two.</p> Signup and view all the answers

    Which of these statements is TRUE regarding the use of AVL trees in the real world?

    <p>AVL trees are widely used in many real-world applications, including databases, search engines, and operating systems, to ensure efficient data management.</p> Signup and view all the answers

    Study Notes

    CS201 Data Structures and Algorithm Design - Lecture 11

    • Binary Search Tree (BST) & AVL Trees This lecture covers binary search trees and AVL trees.

    Lecture Contents

    • Deletion in Binary Search Tree Three cases for deleting nodes in a BST are:

      • Node with zero children (leaf node): Simply delete the node.
      • Node with one child: Connect the child node directly to the parent of the deleted node.
      • Node with two children: Replace the node with its inorder predecessor (largest value in the left subtree) or inorder successor (smallest value in the right subtree).

    • Implementing BST with Python: Includes node creation, insertion, traversal (inorder, preorder, postorder), searching, finding lowest and highest values within the tree.

    • BST Drawbacks: BSTs can become unbalanced, impacting efficiency (time complexity).

    • AVL Trees: A self-balancing BST. Maintains balance by controlling the height differences of subtrees through the balance factor.

    • Balance Factor: Calculated by subtracting the height of the right subtree from the height of the left subtree of a node. A valid AVL tree has balance factors of -1, 0, or 1.

    Deletion Examples

    • Example 1 (Case 1 & 2): Depicts deletion of nodes with zero and one child.

    • Example 2 (Case 3): Shows replacement with the highest or lowest node in the appropriate subtree when deleting a node with two children.

    • Example 3 (Case 3): Deletion of a node with two children, showing replacement with the minimum value in the right subtree.

    • Example 4 (Case 3): Deletion example showing replacement with the maximum value in the left subtree.

    Exercise: Deletion (HW)

    • Includes concrete examples for deletion exercises for practice.

    Using Python: Implementation of Binary Search Tree

    • Code examples and steps for creating a binary search tree using python.

    BST Operations

    • Creation: Demonstrates the creation of a new Node in the binary search tree.

    • Insertion Detailed steps and code snippet for inserting a new node in the BST, handling cases where the value already exists and handling left and right insertions.

    • Traversals: Includes preorder, inorder, and postorder traversals for accessing the contents in a BST

    • Searching: How search works, based on the comparison of the tree node values to the search value.

    • Finding lowest and highest values: Algorithms to locate the minimum and maximum values in a binary tree.

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    Related Documents

    CS201 Data Structures and Algorithms Lecture 11 PDF

    Description

    This lecture focuses on Binary Search Trees (BST) and AVL Trees, covering the deletion process in BSTs, including different cases depending on the node's children. Additionally, it discusses implementing BSTs using Python and addresses the drawbacks of BSTs, particularly their potential to become unbalanced. Finally, an introduction to AVL Trees as self-balancing BSTs is provided.

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